BP-K20D vertical grip and external batteries

I've resumed using my ancient K20D, but its batteries are garbage after so many years. One was wholly useless, so I opened it up and as expected found two 18500 LiIon cells in it.

Re-celling the batteries is always an option, but an annoying one since I don't have any 18500 cells and would have to make an order specifically. I do have plenty of 18650s because I work on e-scooters and e-bikes, but of course they won't fit in the camera's battery receptacle.

Enter: the BP-K20D vertical grip, which I bought when I got the camera but almost never used. It has the option of adding a second battery, and importantly has enough space inside that I could hack two 18650 cells in it.

Problem is, if I only put a battery in that and try to run a camera without a battery in its receptacle, it just flashes the low battery symbol and doesn't work.

Would it make sense to keep one of the degraded batteries in the camera so it registers something present there and turns on?

Or to put it in another way, if I have a bad battery in the camera and a good one in the grip, will it actually run from the one in the grip and not attempt to use the degraded one primarily?